If we're given V=2x^2+2y^2 and we're told to find the field at a point x=3, y=3, would this method be correct?
Ex=d(2x^2)/dx=4x=12
Ey=d(-2y^2)/dy=-4y=-12
Therefore, E={12i - 12j}
Not entirely sure, this is the first of its kind.
Not true for your problem, actually. If you were working in only one dimension, it would be true. For your case, you should have the vector equationAlright, I have yet to encounter that sign so it's probably best if I say E=-dv/dx correct?
Or, for two dimensions, you'd have